There are two major approaches to IR namely Realism and Idealism(liberalism) and if both combined to get maximum advantage of situation is called Eclecticism... As currently U.S is dealing Arab Spring with Eclecticism. Dealing Libiya with realism and some other with idealism or liberalism....

This is what i know something about approaches... there are other approaches to IR also i.e. Feminism(IR) and English School of Thought etc....